You don't even have to do that. Just use paintFX to paint a starfield directly in the perspective view and make sure you paint them at depth. I've done this and animated flythroughs before. Works great.
If you want to map your background on a sphere, just scale your sphere larger so you never encounter the areas that are pinched. Think about where your cameras are going to be placed and focus on those areas.
"Terminat Bora Diem, Terminal Auctor opus."